(i) MBND is a parallelogram, so MD ∥ BN. Applying Theorem 7 to △ABY and △CDX proves the intercepts along AC are equal. (ii) Construct a parallelogram with diagonal PQ, draw parallel lines dividing an auxiliary ray into three parts ...
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Both triangles PCD and QCD share the common base CD and lie between parallel lines AB and CD, giving identical perpendicular heights. Hence their areas are equal, and the ratio area(ΔPCD) : area(ΔQCD) is 1:1.